{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T18:19:42Z","timestamp":1772821182184,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T00:00:00Z","timestamp":1741046400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Muhammadiyah University of Semarang, Indonesia","award":["1927\/UNIMUS\/KP\/2022"],"award-info":[{"award-number":["1927\/UNIMUS\/KP\/2022"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>When handling longitudinal data in regression models, we often encounter problems involving two interrelated response variables. These response variables may display an unknown curve shape in their relationship with one predictor variable, referred to as the nonparametric component, while maintaining a linear relationship with other predictor variables, referred to as the parametric component. In such cases, a Biresponse Semiparametric Regression (BSR) approach is a suitable solution. This research aims to estimate the BSR model for longitudinal data using the Local Polynomial Kernel (LPK) estimator by considering a symmetrical variance\u2013covariance matrix estimate validated on simulation data and apply it to a real dataset of Dengue Hemorrhagic Fever (DHF) disease. The parameter estimation method used is a combination of Least Squares (LS) and Weighted Least Squares (WLS). For determining the optimal bandwidth, we use a Generalized Cross\u2013Validation (GCV) method. The simulation study results indicate that with kernel weighting, employing weights derived from the inverse of the variance\u2013covariance matrix significantly enhances the estimation accuracy of the BSR model. In addition, the results of the estimation for modeling the DHF disease, where platelets and hematocrit are response variables, and hemoglobin and examination time are predictor variables, produced an R-Square value of 92.8%.<\/jats:p>","DOI":"10.3390\/sym17030392","type":"journal-article","created":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T13:31:31Z","timestamp":1741095091000},"page":"392","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Estimation of Biresponse Semiparametric Regression Model for Longitudinal Data Using Local Polynomial Kernel Estimator"],"prefix":"10.3390","volume":"17","author":[{"given":"Tiani Wahyu","family":"Utami","sequence":"first","affiliation":[{"name":"Doctoral Study Program, Faculty of Science and Technology, Airlangga University, Surabaya 60115, Indonesia"},{"name":"Department of Statistics, Faculty of Sciences and Technology, Universitas Muhammadiyah Semarang, Semarang 50273, Indonesia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1592-4671","authenticated-orcid":false,"given":"Nur","family":"Chamidah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Technology, Airlangga University, Surabaya 60115, Indonesia"},{"name":"Research Group of Statistical Modeling in Life Science, Faculty of Science and Technology, Airlangga University, Surabaya 60115, Indonesia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6716-3096","authenticated-orcid":false,"given":"Toha","family":"Saifudin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Technology, Airlangga University, Surabaya 60115, Indonesia"},{"name":"Research Group of Statistical Modeling in Life Science, Faculty of Science and Technology, Airlangga University, Surabaya 60115, Indonesia"}]},{"given":"Budi","family":"Lestari","sequence":"additional","affiliation":[{"name":"Research Group of Statistical Modeling in Life Science, Faculty of Science and Technology, Airlangga University, Surabaya 60115, Indonesia"},{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, The University of Jember, Jember 68121, Indonesia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8393-1270","authenticated-orcid":false,"given":"Dursun","family":"Aydin","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Science, Mu\u011fla S\u0131tk\u0131 Ko\u00e7man University, Mu\u011fla 48000, Turkey"},{"name":"Department of Mathematics, University of Wisconsin, Oshkosh Algoma Blvd, Oshkosh, WI 54901, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,4]]},"reference":[{"key":"ref_1","unstructured":"Gujarati, D. 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